Preheat the oven to 350 degrees F (175 degrees C). Grease the sides and bottoms of two 9-inch metal springform pans.
Beat cake mix, water, vegetable oil, and eggs in a large bowl with an electric mixer on low speed until moistened, about 30 seconds. Increase to medium speed and beat for 2 minutes. Pour into the prepared pans.
Bake in the preheated oven until a toothpick inserted in the centers comes out clean, 23 to 2 minutes.
Cool in the pan for 15 minutes, then remove cakes from the springform pans and cool completely, about 20 more minutes.
Place one cake on a serving tray, forming the bunny's head.
Cut 2 convex-shaped ears from each side of the second cake, and place them on each side of the head to form ears. Place the remaining concave-shaped piece about 1/2 inch below the head for the bowtie.
Frost the entire bunny cake with vanilla frosting; pat the cup coconut evenly over top and sides. Decorate the bunny face and bowtie with jellybeans and use licorice to make whiskers.